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Question

A hollow cylinder, a spherical shell, a solid cylinder and a solid sphere are allowed to roll on a inclined rough surface of coefficient of friction μ and inclination θ. The correct statements are

A
if cylindrical shell can roll on inclined plan, all other objects will also roll
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B
if all the objects are rolling and have same mass, the K.E. of all the objects will be same at the bottom of inclined plane
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C
work done by the frictional force will be zero, if objects are rolling
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D
frictional force will be equal for all the objects, if having same mass
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Solution

The correct options are
A if all the objects are rolling and have same mass, the K.E. of all the objects will be same at the bottom of inclined plane
B if cylindrical shell can roll on inclined plan, all other objects will also roll
C work done by the frictional force will be zero, if objects are rolling

to satisfy the condition of pure rolling

solving this

since
therefore max
thus for cylindrical shell as we know k = 1 which is maximium of all three therefore maximium is offered by the plane and for other two is enough to make them roll.


Work done by friction is always 0 in the case of rolling as we know that point of contact is always at rest.



Applying the conservation of mechanical energy


that total K.E = mgh
also


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